If it turns out the issue is on the board and not the screen, which is very likely, you will have to send it to someone to repair the backlight circuitry. I offer this service here in Australia, but there are people all around the world that can help you.
Basically i expect the issue to be a backlight "filter", or the diode that powers the backlight, which commonly blow when a short or too much current is drawn on the backlight anode line.
Check out the link on my profile to locate someone near you. They all come highly recommended